Hydrogen as an energy carrier represents one of the most promising carbon-free energy solutions. The ongoing development of power-to-gas (PtG) technologies that supports large-scale utilization of hydrogen is therefore expected to support hydrogen economy with a final breakthrough. In this paper, the economic performance of a MW-sized hydrogen system, i.e. a composition of water electrolysis, hydrogen storage, and fuel cell combined heat and power plant (FCCHP), is assessed as an example of hydrogen-based bidirectional electrical energy storage (EES). The analysis is conducted in view of the Danish electricity spot market that has high price volatility due to its high share of wind power. An economic dispatch model is developed as a mixed-integer programming (MIP) problem to support the estimation of variable cost of such a system taking into account a good granularity of the technical details. Based on a projected technology improvement by 2020, sensitivity analysis is conducted to illustrate how much the hydrogen-based EES is sensitive to variations of the hydrogen price and the capacity of hydrogen storage.